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The Kelvin-Helmholtz theorem on conservation of circulations is supposed tohold for ideal inviscid fluids and is believed to be play a crucial role inturbulent phenomena, such as production of dissipation by vortexline-stretching. However, this expectation does not take into accountsingularities in turbulent velocity fields at infinite Reynolds number. Wepresent evidence from numerical simulations for the breakdown of the classicalKelvin theorem in the three-dimensional turbulent energy cascade. Althoughviolated in individual realizations, we find that circulations are stillconserved in some average sense. For comparison, we show that Kelvin's theoremholds for individual realizations in the two-dimensional enstrophy cascade, inagreement with theory. The turbulent ``cascade of circulations'' is shown to bea classical analogue of phase-slip due to quantized vortices in superfluids andvarious applications in geophysics and astrophysics are outlined.Comment: 4 pages, 3 figure

Is the Kelvin Theorem Valid for High Reynolds Number Turbulence?